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A graph is 2-planar if it can be drawn in the plane such that no edge is crossed more than twice. Bekos et al. (2017) completely characterized optimal non-simple 2- and 3-planar graphs, which have edge counts of 5n - 10 and 25n - 11, respectively.
1-planar graph | doublecross graph | k-planar graph | planar graph
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